[填空题]
On 1st of January 2021, Fionad0z7xenu*wule3/ )/k ots)z u (. v+6bet ikrzm*g 8f))m gnqmdecides to take out a bank loan to purchase a new Tesla electric car. Fiona takes out a loan of P dollars with a bank that offers a nominal annual interest rate of 2.6*iv+(m k.bme)grmng8qtzf 6) % , compounded monthly.
The size of Fiona's loan at the end of each year follows a geometric sequence with common ratio, $\alpha$ .
1. Find the value of $\alpha$ , giving your answer to five significant figures.
The bank lets the size of Fiona's loan increase until it becomes triple the size of the original loan. Once this happens, the bank demands that Fiona pays the entire amount back to close the loan.≈
2. Find the year during which Fiona will need to pay back the loan.
